Tate Modern's Rothko exhibition is a great show, and I say that as someone who is not much drawn to the artist, and especially not to the aura of religiosity that hangs over his work. Rothko was a painter, not a religion, and the curator, Achim Borchardt-Hume, has made an effort to rescue Rothko from his fans - even, perhaps, from himself.

At the heart of the exhibition is a large selection from the cycle of paintings originally commissioned as murals for the Four Seasons restaurant in New York, in Mies Van der Rohe and Philip Johnson's 1957 Seagram building on Park Avenue. In 1958, Rothko hired a studio in which he could duplicate the proportions of the restaurant. But instead of committing himself to a specific suite of canvases, he made more than 30 large works of varying sizes. Eventually he pulled out of the commission, and later donated a number of the paintings to the Tate, devising a room plan for their display. Like Rothko's plans for the restaurant itself, the final choice and arrangement of works was never finalised, although a Rothko Room (as it has come to be known) is almost always on view somewhere at Tate.

The Tate's own holdings of this group are augmented here by paintings from the Kawamura Memorial Museum in Japan and museums in the US. Hung high on the walls, and lit at a higher wattage than is usual, the paintings can now be seen afresh - though fresh is not exactly the word. Some have not worn well, and have suffered poor restoration and relining at certain points in their histories. But this happens: paintings change their appearance throughout their sometimes long and eventful lives. In any case, these problems are part of the paintings - they give us an insight into Rothko's working process, which is intimately linked to his thinking, to his fantasies about what a painting is, what it could do, how it could exist.

The show makes a careful study of Rothko's technique, his materials and paint application. One painting, owned by the Tate, is shown alongside close-up photographs of details seen under ultraviolet light, revealing the complex layerings and reworkings the artist subjected his work to. The painting is displayed on a false wall, with an aperture behind that enables us to see the back of the canvas.

With their plum and red grounds, their orange and russet and grey and brownish hovering forms, the Seagram paintings always risked being taken for an overly tasteful colour scheme. Their mutedness can seem a kind of deluxe sumptuousness, to offset the brownish tinted windows of the Seagram building. On a bad day, and to an unsympathetic eye, Rothko can look cheap rather than deep. But he was also an intensely dissatisfied artist, who at his best pushed his paintings beyond his innate taste. He kept on working until the works became unfamiliar to him, as awkward in the world as he probably felt in his own skin. For all their premeditation, Rothko's approach to the Seagram paintings is often revealed in blunt and even slapdash touches and swipes of his house-painter's brush.

The dim lighting and contained feeling of the Rothko Room at the Tate has always given it, for some spectators, an air of immanence and mystery. I prefer paintings in plain sight, without the heavy breathing, never mind the intimations of tragedy in the shape of Rothko's suicide at the age of 66. His death tends to obscure his achievements even more than the peculiarly low light levels he preferred for the work's display. Rothko is supposed to have said that he wanted people to cry when they looked at his paintings, and that he wanted his work to be miraculous. But artists are sometimes their own worst advocates, and Rothko's remarks seem to have become more portentous and bellicose as other artists overtook the first alumni of the New York school, the so-called abstract expressionists.

Rothko was interested in the simplified forms that inhabited his paintings, the spread of pigment across the canvas, and how different coloured areas meet; he was also much concerned with the layering of his paintings, from the bare canvas up. He painted from the inside out. Atmospheric photographs of the artist have him seated before an incomplete canvas, smoking and looking into the painted void. Somewhere in the world, an abstract painter is undoubtedly doing the same thing right now. The difference is that it is impossible to do this today without method-acting Rothko. Even he staged these scenes, for the photographer Hans Namuth.

During the 1960s, Rothko's paintings become poised between the materiality of their surfaces and forms, and the emergence of an image, even if it is an image of nothingness, or an image denied: a blank black screen, or a simple near-horizontal division which we unavoidably see as a horizon, between grey and brown, or black and grey. Rothko cut out the clutter, and in his later work tried to make every single thing count. Someone once said of American abstract painting that Barnett Newman closed the door, Rothko pulled down the blind and Ad Reinhardt turned off the light. Rothko was much vexed by Reinhardt's black-on-black paintings, with their exquisite impenetrability, their cruciform shapes revealed only as one's eyes grow attuned to their close tones. Rothko was undoubtedly jealous of them, and even had an affair with Reinhardt's widow.

While he could never be seen as a minimalist, Rothko's insistence on his Nietzschean individuality did not make him impervious to other artists' work, or even immune to fashion. The stripped-down formats and the blacks and greys of his later works find many parallels in the art of their time, and in particular the work of younger generations of artists both in New York and Europe. Rothko's late paintings may look as if they emerged from some mysterious cave, but he didn't live in one.

He did, however, retreat to his studio in the last year of his life, having separated from his wife. He had heart trouble and emphysema, and drank and smoked too much. He tried to set up a salon in his studio, but the younger artists who came proved uncongenial to him. Maybe they brought too much of the world in with them. Here he painted the works that occupy the last two rooms of the Tate show.

There are fewer than 40 paintings exhibited at Tate Modern, give or take some smaller studies and a few photographs. This allows us to concentrate on individual works, all of which bear close scrutiny and demand time, even though little seems to be happening in them. The paradox is that the more hermetic and emptied-out Rothko's last works seem, and the more similar to one another they become, the more crucial every single detail gets. These paintings stop being Rothko's and become entirely themselves. We see that Rothko smeared into the grey in the lower portion of the paintings with his fingers, rubbing out areas of paint, as though he were rubbing fog from a window with his sleeve, only to reveal more fog outside. He applied water or solvent, as if to unpaint the built-up surface. The later works in acrylic cannot, in any case, stand having too much paint on them. As the paint gets thicker, it begins to acquire a nasty plastic sheen, like a vinyl car seat, which Rothko wanted to avoid. Every single thing that Rothko did and undid to these last paintings matters. They refuse to be the landscapes they at first resemble. In a way, they are unreadable propositions.

These are his best works. But walk out of the show and you are plunged straight into merchandise: T-shirts, and winter scarves in Rothko reds and browns. Rarely have I seen merchandising so at odds with the spirit of any artist's work, and so impervious to the curatorial drive of the exhibition - even if the show gives us Rothko the materialist, not Rothko the religion.